The invention relates to an apparatus and a method for determining an approximate value for the stroke volume and the cardiac output of a person""s heart. The apparatus and method employ a measured electrical impedance, or admittance, of a part of a person""s body, namely, the thorax. This part of a person""s body is chosen because its electrical impedance, or admittance, changes with time as a consequence of the periodic beating of the heart. Accordingly, the measured electrical admittance or impedance can provide information about the performance of the heart as a pump.
In 1966, Kubicek et al. were the first to design a clinically applicable device, capable of determining the stroke volume (SV) by non-invasive, electrical means. The Kubicek method is disclosed in the article by Kubicek et al., Development and Evaluation of an Impedance Cardiac Output System, Aerospace Medicine 1966, pp 1208-1212, and in U.S. Pat. No. 3,340,867 which are both incorporated herein by reference. (see also U.S. Pat. No. 5,178,154 to Ackmann et al, U.S. Pat. No. 5,316,004 to Chesney et al, U.S. Pat. No. 4,953,556 to Evans, U.S. Pat. No. 5,685,316 to Schookin et al, U.S. Pat. No. 5,505,209 to Reining, U.S. Pat. No. 5,529,072 to Sramek, U.S. Pat. No. 5,503,157 to Sramek, U.S. Pat. No. 5,469,859 to Tsoglin et al, U.S. Pat. No. 5,423,326 to Wang et al, and U.S. Pat. No. 5,309,917 to Wang et al.)
When a tetrapolar array of circumferential band electrodes is placed at the base of the neck and about the circumference of the lower chest, at the level of the xiphoid process, and a constant magnitude alternating current (AC) is injected through the upper cervical and lower thoracic band electrodes, a voltage, proportional to the thoracic electrical impedance (or reciprocally proportional to the admittance), is measured between the inner cervical and thoracic band electrodes. The portion of the cardiac synchronous impedance change, xcex94Z(t), temporally concordant with stroke volume, was ascribed solely and uniquely to volume (plethysmographic) changes of the aorta during expansion and contraction over the heart cycle.
In the article by Woltjer H. H. et al. (The technique of impedance cardiography. Eur Heart J 1977; 18: 1396-1403), the Kubicek model is explained as follows. The aorta is considered a cylinder of length L, equal to the distance between the voltage sensing electrodes. The thorax, exclusive of the aorta, is considered a cylinder of length L, equal to aortic length, and of cross-sectional area (CSA), equal to the cross-sectional area of the thorax measured at the xiphoid level. The blood-filled aorta is assumed to have a constant specific electrical resistance equal to that of stationary blood, xcfx81. The thoracic encompassing cylinder is assumed to be homogeneously perfused with blood of specific resistance xcfx81. The aorta and the thoracic encompassing cylinder are assumed to be analogous to parallel electrical conductors.
It was accepted by Kubicek that, according to Nyboer (J. Electrical impedance plethysmography. A physical and physiologic approach to peripheral vascular study. Circulation 1950; 2: 811-821), the portion of xcex94Z(t), temporally concordant with SV, represented simultaneous inflow and outflow of blood over the systolic portion of the heart cycle. Thus, determining the area underneath the systolic portion of xcex94Z(t) was assumed not to represent net volume inflow across the aortic segment under electrical interrogation. Thus, an extrapolation procedure was proposed, utilizing the maximum forward systolic slope of xcex94Z(t). In order to compensate for aortic outflow, the maximum forward slope, analogous to peak flow, was stipulated to be constant throughout the systolic ejection interval. The maximum forward systolic upslope represents the peak, or maximum rate of change of impedance, i.e.             (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MAX    .
Instead of measuring the slope directly, as proposed by Nyboer, Kubicek electronically differentiated xcex94Z(t) into dZ(t)/dt. Thus, the peak systolic magnitude of dZ(t)/dt is             (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MAX    .
In order to derive stroke volume (SV), Kubicek multiplied the peak rate of change of impedance by systolic flow time of the left ventricle, TLVE.
According to Kubicek       SV    =                            V          eff                ·                                            (                                                ⅆ                                      Z                    ⁢                                          (                      t                      )                                                                                        ⅆ                  t                                            )                        MAX                                Z            0                          ·                  T          LVE                    =              ρ        ⁢                  xe2x80x83                ⁢                                            L              2                                      Z              0                                ·                                                    (                                                      ⅆ                                          Z                      ⁢                                              (                        t                        )                                                                                                  ⅆ                    t                                                  )                            MAX                                      Z              0                                ·                      T            LVE                                ,
wherein Z0 is the quasi-static portion of the measured impedance Z, and wherein       (                  ⅆ                  Z          ⁢                      (            t            )                                      ⅆ        t              )    MAX
is the peak value of the (inverted) first time-derivative of xcex94Z(t), which corresponds to the maximum forward systolic upslope of xcex94Z(t). Note that in this context, by peak magnitude, the maximum absolute amplitude is stipulated. In fact, during systole, the impedance decreases such that the sign of xcex94Z(t) is negative. Hence, correctly stated,       (                  ⅆ                  Z          ⁢                      (            t            )                                      ⅆ        t              )    MAX
is the minimum of the time-derivative of xcex94Z(t), i.e.             (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MIN    .
Furthermore, in the above formula, TLVE is the left ventricular ejection time, i.e. the time between opening and closure of the aortic valve, also referred to as systolic flow time. The volume       V    EFF    =      ρ    ·                  L        2                    Z        0            
is the volume of electrically participating thoracic tissue (VEPT), wherein xcfx81 is the specific resistance of stationary blood, which Kubicek assumed to be 150 xcexa9cm, and L is the distance between the voltage-sensing electrodes which are applied to the neck and thorax.
By virtue of rigid theoretical constraints, the Kubicek method, and its derivatives, consider volume changes in the aorta, i.e. plethysmographic changes, to be the sole contributor to             (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MAX    .
Consequently, xcex94Z(t) is assumed to represent the time-variable volumetric expansion and recoil of the aorta. Thus, its time-derivative, dZ(t)/dt, represents an ohmic equivalent of the rate of change of aortic volume. This would also imply that             (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MAX    ,
measured in [xcexa9/s], is directly proportional to peak flow [mL/s] and peak velocity [cm/s].
It is widely believed that the assumptions made in the Kubicek model are generally valid, i.e. that the increased aortic volume during mechanical systole leads to the decrease in the thoracic impedance. Since Kubicek assumed a directly proportional, i.e. linear, relationship between SV and       (                  ⅆ                  Z          ⁢                      (            t            )                                      ⅆ        t              )    MAX
times TLVE, it is usually believed that       (                  ⅆ                  Z          ⁢                      (            t            )                                      ⅆ        t              )    MAX
is analogous and proportional to peak flow, or peak rate of change of aortic volume. Therefore, subsequent improvements focused only on a better definition and modeling of VEFF.
For example, Sramek developed a formula according to which       V    EFF    =            L      3        4.25  
(see U.S. Pat. No. 4,450,527 which is incorporated herein by reference).
In a later iteration, Sramek approximated L as 17% of the person""s height h. Thus, Sramek proposed the equation   SV  =                              (                      0.17            ⁢            h                    )                3            4.25        ·                            (                                    ⅆ                              Z                ⁢                                  (                  t                  )                                                                    ⅆ              t                                )                MAX                    Z        0              ·          T      LVE      
Bernstein (Bernstein D. P., A new stroke volume equation for thoracic electrical bioimpedance. Crit Care Med 1986; 14: 904-909) introduced a factor xcex4 accounting for the person""s weight deviation from ideal (as determined from the Metropolitan Life Insurance tables), corrected for blood volume, normalized to deviation from ideal body weight. Otherwise, Sramek""s model remained unchanged, and Bernstein proposed the formula   SV  =      δ    ·                            (                      0.17            ⁢            h                    )                3            4.25        ·                            (                                    ⅆ                              Z                ⁢                                  (                  t                  )                                                                    ⅆ              t                                )                MAX                    Z        0              ·          T      LVE      
Despite these various efforts for improving the determination of the stroke volume, the stroke volume could not be correctly predicted across a wide range of subjects in health and disease.
In particular, in the following cases, the Sramek-Bernstein equation generally results in an overestimation of the true predicted stroke volume: children and healthy young adults; underweight individuals; tall, thin adults.
According to Spiering et al (Comparison of impedance cardiography and dye dilution methods for measuring cardiac output. Heart 1998; 79: 437-441), the use of the Sramek-Bernstein equation generally results in an underestimation of the true predicted stroke volume in the following cases: elderly adults, obese individuals; individuals with sepsis, acute lung injury or pulmonary edema; and during exercise.
It is therefore an object of the invention to provide apparatus and method that determines the stroke volume accurately for individuals of all ages in health and disease states.
The invention considers the absolute peak rate of change of impedance,       "LeftBracketingBar"                  (                              ⅆ                          Z              ⁢                              (                t                )                                                          ⅆ            t                          )            MIN        "RightBracketingBar"    ,
to be the ohmic equivalent of peak aortic blood acceleration [mL/s2], or peak rate of change of aortic blood velocity. As a consequence, xcex94Z(t), in earliest systole, is related to hemorheologic (blood flow) changes, not plethysmographic (volume) changes. Thus, the new apparatus can be described as an xe2x80x98electrical velocimeterxe2x80x99, or the method incorporated as xe2x80x98electrical velocimetryxe2x80x99.
Consequently, the measured value of   "LeftBracketingBar"            (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MIN    "RightBracketingBar"
cannot be implemented directly into SV calculation. Theoretically,   "LeftBracketingBar"            (                        ⅆ                      Z            ⁢                          (              t              )                                                ⅆ          t                    )        MIN    "RightBracketingBar"
must be integrated in order to obtain an ohmic equivalent for blood velocity. In summary, the invention mandates that the part of the previous art related to       "LeftBracketingBar"                  (                              ⅆ                          Z              ⁢                              (                t                )                                                          ⅆ            t                          )            MIN        "RightBracketingBar"        Z    0  
be changed.
Hence, the apparatus and method according to the invention employ no underlying modeling or theoretical assumptions of the Kubicek, or any other subsequent, plethysmographic approaches.
According to theory derived from basic science (and published as Sakamoto K, Kanai K. Electrical characteristics of flowing blood. IEEE Trans Biomed Eng 1979; 26: 686-695; Visser K R. Electrical properties of flowing blood and impedance cardiography. Ann Biomed Eng 1989; 17: 463-473; Lamberts R et al. Impedance cardiography. Assen, The Netherlands: Van Gorcum 1984; 84-85; and Matsuda Y et al. Assessment of left ventricular performance in man with impedance cardiography. Jap Circ J 1978; 42: 945-954), the change of blood resistivity, and the rate of change of blood resistivity, can be normalized for corrected flow time, FTC,             FT      C        =                  T        LVE                    T        RR        m              ,
where TLVE equals the left-ventricular ejection time (known also as systolic flow time), divided by a root of TRR, where TRR equals the value for the RR interval (cycle time) in seconds.
With VEFF defined as the effective volume of electrical participating thoracic tissue ([VEFF]=ml), the stroke volume SV, according to the invention, is calculated according to the formula   SV  =            V      EFF        ·          xe2x80x83        ⁢                            C          1                (                              "LeftBracketingBar"                                          (                                                      ⅆ                                          Z                      ⁡                                              (                        t                        )                                                                                                  ⅆ                    t                                                  )                            MIN                        "RightBracketingBar"                                Z            0                          )            n        ·                  (                  1                      T            RR                          )            m        ·          T      LVE      
with 0.15 less than n less than 0.8 and 0xe2x89xa6mxe2x89xa61.5, and wherein C1 is a constant which is necessary if n+mxe2x89xa01 in order to adjust the units of the measured values in the formula such that the stroke volume is obtained in milliliters. C1 need not have a numerical value different from 1.
A preferred case is that n=1xe2x88x92m. Then, C1=1.
The most preferred case is n=m=0.5. Then,       FT    C    =                    T        LVE                              T          RR                      .  
Other objects, features and advantages of the invention will become apparent from the following description of a preferred embodiment of the invention.